Related papers: Integral functionals on Sobolev spaces having mult…

The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate…

In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations

We study the relaxation of multiple integrals of the calculus of variations, where the integrands are nonconvex with convex effective domain and can take the value \infty. We use local techniques based on measure arguments to prove integral…

In this paper we study the regularity of the local minima of integral functionals: in particular, not convexity (quasi-convexity, policonvexity or rank one convexity) hypothesis will be made on the density, neither structure hypothesis nor…

We prove an a priori estimate for the second derivatives of local minimizers of integral functionals of calculus of variation with convex integrand with respect to the gradient variable, assuming that the function that measures the…

In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.

In this paper we study the everywhere H\"oder continuity of the minima of a class of vectorial integral funcionals

The present note contains a review of $p$-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of…

In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations

The present work constitutes a first step towards establishing a systematic framework for treating variational problems that depend on a given input function through a mixture of its derivatives of different orders in different directions.…

We consider general integral functionals on the Sobolev spaces of multiple valued functions, introduced by Almgren. We characterize the semicontinuous ones and recover earlier results of Mattila as a particular case. Moreover, we answer…

We present a simple proof of the continuity, in the sense distributions, of the minors of the differential matrices of mappings belonging to grand Sobolev spaces. Such function spaces were introduced in connection with a problem on minimal…

We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…

We give an overview of some applications of a general variational principle.

We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces

This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…

Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…

Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive…

We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional…